Tobias Hill doesn't have a mobile phone. He doesn't do Twitter, and he doesn't do Facebook, and he doesn't text because, without a phone, he can't. He has just got a website. It has, he explains, taken four years to get it up. "I'm not a technophobe," he says. "I think it's all rather incredible. But I think the business of the writer is to write." And write he has. Now aged 43 he is a prizewinning and critically acclaimed author of five novels, four volumes of poetry, a short story collection and a children's book.

What Was Promised

by Tobias Hill

He has suggested we meet at Chapel Market, just off Islington's Upper Street in London where there's one stall selling artisan bread and cakes, but mostly the stalls are selling what markets nearly always sell: cheap bags and clothes, fruit and veg, cleaning products, make-up and tat. And a Manze's Eel Pie and Mash Shop.

Hill this place because his new novel, What Was Promised, has a lot to do with markets, and because he once worked in this particular one. "It was the best holiday job I ever had," he tells me. "We'd come out here bright and early and sell our jogging bottoms and Batman T-shirts."

What Was Promised starts off in Columbia Road, of market fame, in 1948. Spanning 40 years, it tells the story of three families brought to the East End by the war. There's Solly Lazarus, the Jewish watchmaker from Danzig, and his beautiful wife, Dora. There's Clarence Malcolm, the "Banana King" from Jamaica, his wife, Bernadette, and Sidney, their son. And there's Michael and Mary Lockhart, originally from Birmingham, who both know not to ask too many questions about the errands Michael's paid to run. Their daughters, Iris and Floss, play with Sidney and with a boy who thinks he must be an orphan, and who says his name is "Pond".

All immigrants of a kind, the characters have to learn, as Clarence puts it, to live on their "wits alone". They live in Columbia Buildings, condemned by the council as a slum. As they struggle to make ends meet, their lives and stories intertwine, first in good ways and then in a terrible way that will change nearly all their lives. The effects of this are still being felt in 1988 when the novel ends.

"Markets are precious," says Hill, "and they're so easily destroyed. And they're not very English, which is why when people got off the boats in 1948, they would see this little slice of life, which could be anywhere. I wanted to get the sense of that and how that felt." Hill, who has been described by this paper as "contemporary literature's renaissance man", seems as comfortable with a 500-page novel as a short story or a poem. He brings his poet's eye for precision to the teeming life of the market. He talks, for example, about air that "tastes of old batteries", rain that "hardens down into the byways", "crizzling down the windows", and about a face "sunken as old meat". But his main theme isn't actually the market but the "collisions" the city throws up. The novel, like his last poetry collection, Nocturne in Chrome and Sunset Yellow, has Emerson's "cities give us collision" as its epigraph. "When people get exhausted by the city and want to escape," he says, "it's the collisions they want to get away from. I have," he adds, "been trying not to write about London for years."

If he's been trying, he hasn't been trying all that hard. In his first collection of short stories, Skin, which won the 1998 PEN/Macmillan award for fiction, he wrote partly about Japan, where he'd been living, but also about London Zoo. His first novel, Underground, published in 1999, as you might guess from the title, is largely set on the underground: and not just in the passages and tunnels that people still use. His next, The Love of Stones, switches between Victorian and contemporary London, as well as Tokyo and Istanbul. The Cryptographer, about a love affair between a tax inspector and "the world's first quadrillionaire" is set in the London of the future. Only his fourth novel The Hidden, published five years ago, is set largely outside London, in Greece.

His first poetry collection, Year of the Dog, which won him an Eric Gregory award in 1995, was, like Skin, dominated by images of Japan. His second, Midnight in the City of Clocks, moves between London and Japan. His third, Zoo, is nearly all about London, and was published while he was poet in residence at London Zoo. Nocturne in Chrome and Sunset Yellow, published in 2006, is pretty much a love song to the city. "London," he says, in the poem "November", "– there's a rhythm to the name, its ending an echo of its beginning, as if London were the name for somewhere full to the brim with its own echoes".

Rhythm is, of course, as central to prose as to poetry, but there's also the rhythm of structure, and plot. Hill's previous four novels could probably be described as "intellectual thrillers": in Underground, the central character is trying to track down the person who's pushing women under trains; in The Love of Stones, she's on a hunt for a missing jewel; in The Cryptographer she's investigating an electronic currency that seems to have been protected by an unbreakable code; and in The Hidden a team of archeologists hide, and eventually reveal, a terrible secret.

"Judgments and secrets are what make a good novel," he says, when I point out the pattern. But you couldn't describe his latest novel as a thriller. Was he trying to get away from the genre? "That," he says carefully, "might be true. People have expectations of what you are as a writer. And writers, on the whole, don't like to be classified. About five years ago, I decided I wanted to write a novel about people, rather than ideas."

"Absolutely!" says Hill. "They're quite right. My strong suits, coming from poetry, will naturally be description, which I love doing. It comes very easily, and possibly structure, up to a point. My weaker suits are character and dialogue, and that's why I've invested four years in this." And what, I ask, about plot? Presumably, with all those thrillers, he had to do some meticulous plotting in advance? Hill shakes his head. "I don't really plot, no. Do you know that lovely Ursula Le Guin book about writing? She talked about her novels having rhythms not like poetry, but huge rhythms, like mountain ranges – and that comes out of not knowing too much. When the plot grows out of the character, that's much harder, because you're constantly gardening, and trying to work out which bit needs to be trimmed."

In the past, Hill has said that he can't write poems and novels at the same time. Now, he does both. "During the last novel," he says, "it was so difficult that halfway through I just caved in, because I was so hungry to write poetry. It helped when I came back to the novel as well." And how different is the process? "I think," he replies, after a pause, "the poem and the short story have an affinity, in that you know it's going to be over soon. With a novel, there is no hurrying it. You're constantly walking into the unknown."

What Was Promised is about outsiders, but then nearly all Tobias Hill's work is about outsiders. His own family is a mixture of German-Jewish and British. His mother's German parents moved to Welwyn Garden City because "they thought in a new town no one would have any roots". His father's family were "goldsmiths and gunmakers and workhouse masters". One of his relatives, he says, "was a dodgy, irascible travelling land surveyor who once chased off an armed sailor with a shotgun and ended up going mad with syphilis".

Hill grew up in a "bookish household" in Kentish Town, north London, with a journalist father who made "intricate model boats" and wrote "rather good poetry" and a graphic designer mother who did "rather good pictures" and sang. As a child, he was obsessed with butterflies, gemstones and dinosaurs. His grandmother, he says, "was an avid collector of things". He hated school – Hampstead school, where Zadie Smith was also a pupil – but he started writing poems as a child, and was published by the time he was 20. Two years later, he went to live for a couple of years in Japan ("like another version of Britain. There's the same introspection, the same ritualistic tendencies, and tea.") When he returned to London, he had decided he was going to be a writer. "I came back with the idea that I would give it a real go, and move back into my old bedroom. I clomped round the house annoying my parents until they finally threw me out."

He met his wife, Hannah, at his father's memorial service when he was 26. In his poem "October", he writes: "I will never have seen enough of you." Now they have 14-month-old Kit. Hill teaches creative writing one day a week, but the rest of the time he writes. It sounds pretty idyllic. No wonder he writes in his poem "November", "all that brilliance was ours".

Hill is warm and polite, yet his work has often been described as clever but cool. "I know what they mean," he says. "I see people occasionally saying the same thing about Kazuo Ishiguro. What I feel about Ishiguro is that he's an intensely emotional writer, and either you get that or you don't. Obviously, I want people to get something out of this novel. I don't," he says, "want them to say I'm cold."